Previous methods usually sample from EBM [1]} with Markov Chain Monte Carlo (MCMC) [2]}, [3]}, [4]}, [5]}, [6]}, [7]}.
Among them, plug-and-play generative models (PPGMs) [8]} and LACE [9]} define latent-space EBMs.
However, MCMC requires inference-time optimization, which is inefficient and requires the off-the-shelf models to be available at inference; this is also the criticism for diffusion models, regardless of being gradient-guided [10]}, [11]} or not [12]}, [13]}, [14]}.
In contrast, PromptGen achieves efficient, feed-forward sampling. Table REF  shows a comparison with previous methods.
Our INN training is similar to that proposed by [15]} to sample from physical systems, which is later used by [16]} to solve inverse problems with two composed INNs. Notably, [15]} and [16]} do not leverage a low-dimensional latent space, and [16]} requires training a separate model for each image sample. In this paper, we use INN to model arbitrary EBMs for various generative models.
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